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# The probability that Mike can win a competition is 1/4, Rob

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Manager
Joined: 24 Jun 2006
Posts: 62
Followers: 1

Kudos [?]: 3 [0], given: 0

The probability that Mike can win a competition is 1/4, Rob [#permalink]  26 Oct 2006, 16:23
The probability that Mike can win a competition is 1/4, Rob winning is 1/3and Ben winning is 1/6. What is the probability of Mike or Rob winning but not Ben

1/6
5/12
7/12
5/6
1
Intern
Joined: 21 Aug 2006
Posts: 39
Location: LA California
Followers: 1

Kudos [?]: 2 [0], given: 0

= (mike wins)and(rob wins)and(ben loses) OR (mike wins)and(rob loses)and(ben loses) OR (mike loses)and(rob wins)and(ben loses)

= (1/4)(1/3)(1-1/6) + (1/4)(1-1/3)(1-1/6) + (1-1/4)(1/3)(1-1/6)

= (1/4)(1/3)(5/6) + (1/4)(2/3)(5/6) + (3/4)(1/3)(5/6)

=5/6[ 1/12 + 2/12 + 3/12]

= 5/6[1/2]

= 5/12
_________________

Solus Intendo
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VP
Joined: 25 Jun 2006
Posts: 1176
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Kudos [?]: 67 [0], given: 0

1/4 + 1/3 - 1/6 = 5/12.

B is right.
Manager
Joined: 25 Sep 2006
Posts: 153
Followers: 1

Kudos [?]: 4 [0], given: 0

Bad question, did not specified the possible winning condition. Who would think that a competition can be won by three people together.
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